Inner products are additive in both slots: $\langle x+y,z\rangle=\langle x,z\rangle+\langle y,z\rangle$ and $\langle x,y+z\rangle=\langle x,y\rangle+\langle x,z\rangle$. In complex spaces additivity still holds; it is scalar multiplication in the first slot that requires conjugation.
Like how this is organised?
Build your own knowledge tree on knowen.md: notes, decisions and tasks in one connected markdown graph, shared with your team and your AI agents.